Research on the motion of single particle in the spring particle model

The spring particle model assumes that the fabric has a uniform density, with identical properties in both warp and weft directions. It also neglects the fabric's thickness, simplifying the structure for simulation purposes. The fabric is represented as a regular grid of particles, where each particle is connected to its neighbors by springs. This approach discretizes the fabric into a network of mass points linked by massless springs, allowing forces to be transmitted through the system. The bending behavior of the fabric is modeled using bending springs, which simulate the material’s flexibility. Bending refers to the fabric’s ability to deform when subjected to forces or moments perpendicular to its plane. This helps introduce shear rigidity and prevents unrealistic folding or distortion within the plane. Shear properties of fabric are typically assessed using two main indicators: shear stiffness and shear hysteresis. Shear stiffness measures the fabric’s resistance to deformation under shear stress, defined as the shear force per unit width per unit area of deformation. Shear hysteresis, on the other hand, reflects the energy loss during the shearing process, calculated as the difference between the loading and unloading curves. When simulating interactions between a virtual probe and fabric, the mechanical model considers the forces acting on the fabric. As the probe makes contact, all mass points are analyzed to determine the closest point of interaction. The force applied to the nearest particle is then used to update the position of the corresponding mass node. Under the influence of the external force from the probe, the particle moves in the opposite direction, mimicking real-world physical responses. The motion of the particles is governed by Newton’s second law, assuming the spring system behaves linearly. When a spring is stretched or compressed, it exerts a restoring force according to Hooke’s law. As one particle moves due to an external force, the connected particles are affected by the resulting tension or compression. This dynamic interaction leads to the overall deformation of the virtual fabric, with each particle shifting to a new position based on the forces acting upon it. This detailed simulation allows for realistic fabric behavior in virtual environments.

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